Mathematics Colloquia and Seminars

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Indecision and its uses


Speaker: Marty Scharlemann, UC Santa Barbara
Location: 693 Kerr
Start time: Mon, Oct 25 2004, 4:10PM

To understand the structure of a 3-manifold it is useful to understand the surfaces it contains. Particularly helpful are surfaces that can't be simplified (called "incompressible" surfaces). But what if there are no such surfaces? Instead of incompressible surfaces, it is sometimes possible to use surfaces that are extremely compressible. The idea is this: finding it hard to decide how to compress can substitute for not being able to compress at all. If time allows, I'll also discuss the natural analogue for this phenomenon in knot theory.